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Get the answer to your homework problem. Try Numerade free for 7 days We don’t have your requested question, but here is a suggested video that might help. Related QuestionIf the Moon were 2 times closer to Earth than it is now, the gravitational force between Earth and the Moon would be a. 2 times stronger. b. 4 times stronger. a. 2 times stronger. b. 4 times stronger.
DiscussionYou must be signed in to discuss. Video Transcriptthe force of gravity between two objects is approximately inversely proportional toe, one over the radius squared or distance squared. So if you have the moon and the earth a certain distance apart, there's a certain amount of gravitational attraction between them. If you make the moon twice as close to the earth, so kind that distance in half twice is close. So the race will be half assed much, and overall, the force of gravity will become four times stronger because the closer you get to the object is stronger than gravity, so the distance becomes half than the force will become four times as strong. Learning ObjectivesBy the end of this section, you will be able to:
Newton’s laws of motion show that objects at rest will stay at rest and those in motion will continue moving uniformly in a straight line unless acted upon by a force. Thus, it is the straight line that defines
the most natural state of motion. But the planets move in ellipses, not straight lines; therefore, some force must be bending their paths. That force, Newton proposed, was gravity. Fgravity=GM1M2R2\displaystyle{F}_\text{gravity}=G\frac{M_{1}M_{2}}{R^{2}} where Fgravity is the gravitational force between two objects, M1 and M2 are the masses of the two objects, and R is their separation. G is a constant number known as the universal gravitational constant, and the equation itself symbolically summarizes Newton’s universal law of gravitation. With such a force and the laws of motion, Newton was able to show
mathematically that the only orbits permitted were exactly those described by Kepler’s laws. Example 1: Calculating WeightBy what factor would a person’s weight at the surface of Earth change if Earth had its present mass but eight times its present volume? Show Answer With eight times the volume, Earth’s radius would double. This means the gravitational force at the surface would reduce by
a factor of (1/2)2 = 1/4, so a person would weigh only one-fourth as much. Check Your LearningBy what factor would a person’s weight at the surface of Earth change if Earth had its present size but only one-third its present mass? Show Answer With one-third its present mass, the gravitational force at the surface would reduce by a factor of 1/3, so a person would weight only one-third as much. Gravity is a "built-in"
property of mass. Whenever there are masses in the universe, they will interact via the force of gravitational attraction. The more mass there is, the greater the force of attraction. Here on Earth, the largest concentration of mass is, of course, the planet we stand on, and its pull dominates the gravitational interactions we experience. But everything with mass attracts everything else with mass anywhere in the universe. When falling, they are in free fall and accelerate at the same rate as everything around them, including their spacecraft or a camera with which they are taking photographs of Earth. When doing so, astronauts experience no additional forces and therefore feel "weightless." Unlike the falling elevator passengers, however, the astronauts are falling around Earth, not to Earth; as a result they will continue to fall and are said to be "in orbit" around Earth (see the next section for more about orbits). Orbital Motion and MassKepler’s laws describe the orbits of the objects whose motions are described by Newton’s laws of motion and the law of gravity. Knowing that gravity is the force that attracts planets toward the Sun, however, allowed Newton to rethink Kepler’s third law. Recall that Kepler had found a relationship between the orbital period of a planet’s revolution and its distance from the Sun. But Newton’s formulation introduces the additional factor of the masses of the Sun (M1) and the planet (M2), both expressed in units of the Sun’s mass. Newton’s universal law of gravitation can be used to show mathematically that this relationship is actually a3=(M1+ M2)×P2{a}^{3}=\left({M}_{1}+{M}_{2}\right)\times{P}^{2} where a is the semimajor axis and P is the orbital period. Example 2: Calculating the Effects of GravityA planet like Earth is found orbiting its star at a distance of 1 AU in 0.71 Earth-year. Can you use Newton’s version of Kepler’s third law to find the mass of the star? (Remember that compared to the mass of a star, the mass of an earthlike planet can be considered negligible.) Show Answer Check Your LearningSuppose a star with twice the mass of our Sun had an earthlike planet that took 4 years to orbit the star. At what distance (semimajor axis) would this planet orbit its star? Show Answer Again, we can neglect
the mass of the planet. So M1 = 2 and P = 4 years. The formula is a3 = M1 × P2, so a3 = 2 × 42 = 2 × 16 = 32. So a is the cube root of 32. To find this, you can just ask Google, "What is the cube root of 32?" and get the answer 3.2 AU. You might like to try a simulation that lets you move the Sun, Earth, Moon, and space station to see the effects of changing their distances on their gravitational forces and orbital paths. You can even turn off gravity and see what happens. Key Concepts and SummaryGravity, the attractive force between all masses, is what keeps the planets in orbit. Newton’s universal law of gravitation relates the gravitational force to mass and distance: Fgravity=GM1M2R2\displaystyle{F}_\text{gravity}=G\frac{M_{1}M_{2}}{R^{2}} The force of gravity is what gives us our sense of weight. Unlike mass, which is constant, weight can vary depending on the force of gravity (or acceleration) you feel. When Kepler’s laws are reexamined in the light of Newton’s gravitational law, it becomes clear that the masses of both objects are important for the third law, which becomes a3 = (M1+ M2) × P2.
Mutual gravitational effects permit us to calculate the masses of astronomical objects, from comets to galaxies. Glossarygravity: the mutual attraction of material bodies or particles Licenses and AttributionsWhat would happen if Earth had twice the gravity?If gravity were twice as strong , bodies possessing the same construction and mass as our flora and fauna would weigh twice as much and would collapse. It'd be "timber!" for tall, thick trees such as redwoods.
How much bigger or smaller would the force of gravity attracting Earth to the Sun be if the Earth were twice as far from the Sun as it is now?In other words, if a planet were twice as far from the Sun, the force would be (1/2)2, or 1/4 as large. Put the planet three times farther away, and the force is (1/3)2, or 1/9 as large.
What would happen to the gravitational force if Earth doubled in mass?If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on.
What would happen if the force of gravity between the Sun and Earth were turned off?Gravity is the force that pulls Earth and stops it from going off in some other direction.” Without the sun's gravitational pull, Earth would move in a straight line away from the sun. Gravity is also the force that keeps the moon revolving around Earth.
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